A collective name may be used as a general name when it is extended on the ground of what is common to all such totalities as it designates.

"An excited mob is dangerous;" "An army without discipline is useless." The collective name is then "connotative" of the common characters of the collection.

MATERIAL OR SUBSTANTIAL NAMES. The question has been raised whether names of material, gold, water, snow, coal, are general or collective singular. In the case of pieces or bits of a material, it is true that any predicate made concerning the material, such as "Sugar is sweet,"

or "Water quenches thirst," applies to any and every portion. But the separate portions are not individuals in the whole signified by a material name as individuals are in a class. Further, the name of material cannot be predicated of a portion as a class name can be of an individual. We cannot say, "This is a sugar". When we say, "This is a piece of sugar," sugar is a collective name for the whole material.

There are probably words on the borderland between general names and collective names. In such expressions as "This is a _coal_," "The bonnie _water_ o' Urie," the material name is used as a general name. The real distinction is between the distributive use and the collective use of a name; as a matter of grammatical usage, the same word may be used either way, but logically in any actual proposition it must be either one or the other.

ABSTRACT NAMES are names for the common attributes or concepts on which classes are constituted. A concrete name is a name directly applicable to an individual in all his attributes, that is, as he exists in the concrete. It may be written on a ticket and pinned to him. When we have occasion to speak of the point or points in which a number of individuals resemble one another, we use what is called an abstract name. "Generous man," "clever man," "timid man," are concrete names; "generosity," "cleverness," "timidity," are abstract names.

It is disputed whether abstract names are connotative. The question is a confused one: it is like asking whether the name of a town is municipal. An abstract name is the name of a connotation as a separate object of thought or reference, conceived or spoken of in abstraction from individual accidents. Strictly speaking it is notative rather than _con_notative: it cannot be said to have a connotation because it is itself the symbol of what is called the connotation of a general name.[4]

The distinction between abstract names and concrete names is virtually a grammatical distinction, that is, a distinction in mode of predication. We may use concrete names or abstract names at our pleasure to express the same meaning. To say that "John is a timid man" is the same thing as saying that "Timidity is one of the properties or characteristics or attributes of John". "Pride and cruelty generally go together;" "Proud men are generally cruel men."

General names are predicable of individuals because they possess certain attributes: to predicate the possession of those attributes is the same thing as to predicate the general name.

Abstract forms of predication are employed in common speech quite as frequently as concrete, and are, as we shall see, a great source of ambiguity and confusion.

[Footnote 1: It has been somewhat too hastily assumed on the authority of Mansel (Note to Aldrich, pp. 16, 17) that Mill inverted the scholastic tradition in his use of the word _Connotative_. Mansel puts his statement doubtfully, and admits that there was some licence in the use of the word Connotative, but holds that in Scholastic Logic an adjective was said to "signify _primarily_ the attribute, and to _connote_ or _signify secondarily_ ([Greek: prossemainein]) the subject of inhesion". The truth is that Mansel's view was a theory of usage not a statement of actual usage, and he had good reason for putting it doubtfully.

As a matter of fact, the history of the distinction follows the simple type of increasing precision and complexity, and Mill was in strict accord with standard tradition. By the Nominalist commentators on the _Summulae_ of Petrus Hispanus certain names, adjectives grammatically, are called _Connotativa_ as opposed to _Absoluta_, simply because they have a double function. White is connotative as signifying both a subject, such as Socrates, of whom "whiteness" is an attribute, and an attribute "whiteness": the names "Socrates"

and "whiteness" are Absolute, as having but a single signification. Occam himself speaks of the subject as the primary signification, and the attribute as the secondary, because the answer to "What is white?" is "Something informed with whiteness," and the subject is in the nominative case while the attribute is in an oblique case (_Logic_, part I.

chap. x.). Later on we find that Tataretus (_Expositio in Summulas_, A.D. 1501), while mentioning (Tract. Sept. _De Appellationibus_) that it is a matter of dispute among Doctores whether a connotative name _connotat_ the subject or the attribute, is perfectly explicit in his own definition, "Terminus connotativus est qui praeter illud pro quo supponit connotat aliquid adjacere vel non adjacere rei pro qua supponit" (Tract. Sept. _De Suppositionibus_). And this remained the standard usage as long as the distinction remained in logical text-books. We find it very clearly expressed by Clichtoveus, a Nominalist, quoted as an authority by Guthutius in his _Gymnasium Speculativum_, Paris, 1607 (_De Terminorum Cognitione_, pp. 78-9). "Terminus absolutus est, qui solum illud pro quo in propositione supponit, significat.

Connotativus autem, qui ultra idipsum, aliud importat." Thus _man_ and _animal_ are absolute terms, which simply stand for (supponunt pro) the things they signify. _White_ is a connotative name, because "it stands for (supponit pro) a subject in which it is an accident: and beyond this, still signifies an accident, which is in that subject, and is expressed by an abstract name". Only Clichtoveus drops the verb _connotat_, perhaps as a disputable term, and says simply _ultra importat_.

So in the Port Royal Logic (1662), from which possibly Mill took the distinction: "Les noms qui signifient les choses comme modifiees, marquant premierement et directement la chose, quoique plus confusement, et indirectement le mode, quoique plus distinctement, sont appeles _adjectifs_ ou _connotatifs_; comme rond, dur, juste, prudent" (part i. chap ii.).

What Mill did was not to invert Scholastic usage but to revive the distinction, and extend the word connotative to general names on the ground that they also imported the possession of attributes. The word has been as fruitful of meticulous discussion as it was in the Renaissance of Logic, though the ground has changed. The point of Mill's innovation was, premising that general names are not absolute but are applied in virtue of a meaning, to put emphasis on this meaning as the cardinal consideration. What he called the connotation had dropped out of sight as not being required in the Syllogistic Forms. This was as it were the point at which he put in his horn to toss the prevalent conception of Logic as Syllogistic.

The real drift of Mill's innovation has been obscured by the fact that it was introduced among the preliminaries of Syllogism, whereas its real usefulness and significance belongs not to Syllogism in the strict sense but to Definition. He added to the confusion by trying to devise forms of Syllogism based on connotation, and by discussing the Axiom of the Syllogism from this point of view. For syllogistic purposes, as we shall see, Aristotle's forms are perfect, and his conception of the proposition in extension the only correct conception. Whether the centre of gravity in Consistency Logic should not be shifted back from Syllogism to Definition, the latter being the true centre of consistency, is another question. The tendency of Mill's polemic was to make this change. And possibly the secret of the support it has recently received from Mr. Bradley and Mr. Bosanquet is that they, following Hegel, are moving in the same direction.

In effect, Mill's doctrine of Connotation helped to fix a conception of the general name first dimly suggested by Aristotle when he recognised that names of genera and species signify Quality, in showing what sort a thing is. Occam carried this a step farther towards clear light by including among Connotative Terms such general names as "monk," name of classes that at once suggest a definite attribute. The third step was made by Mill in extending the term Connotation to such words as "man," "horse," the _Infimae Species_ of the Schoolmen, the Species of modern science.

Whether connotation was the best term to use for this purpose, rather than extension, may be questioned: but at least it was in the line of tradition through Occam.]

[Footnote 2: The history of the definition of the _Proprium_ is an example of the tendency of distinctions to become more minute and at the same time more purposeless. Aristotle's [Greek: idion] was an attribute, such as the laugh of the man or the bark of the dog, common to all of a class and peculiar to the class (_quod convenit omni soli et semper_) yet not comprised in the definition of the class. Porphyry recognised three varieties of [Greek: idia] besides this, four in all, as follows:--(1) an attribute peculiar to a species but not possessed by all, as knowledge of medicine or geometry; (2) possessed by a whole species but not peculiar to it, as being a biped in man; (3) peculiar to a species, and possessed by all at a certain time, as turning grey in old age; (4) Aristotle's "proprium," peculiar and possessed by all, as risibility. The idea of the Proprium as deducible from or consequent on the essence would seem to have originated in the desire to find something common to all Poryphyry's four varieties.]

[Footnote 3: It is a plausible contention that in the case of the Singular name the extension is at a minimum and the intension at a maximum, the extension being one individual, and the intension the totality of his attributes. But this is an inexact and confused use of words. A name does not _extend_ beyond the individual except when it is used to signify one or more of his prominent qualities, that is, is used with the function of a general name. The _ex_tension of a Singular name is zero: it has no extension. On the other hand, it suggests, in its function as a Singular name, no properties or qualities; it suggests only a subject; _i.e._, it has no intension. The ambiguity of the term Denotation helps the confusion in the case of Singular names. "Denote" in common speech means to indicate, to distinguish. But when in Logic we say that a general name denotes individuals, we have no thought of indicating or distinguishing: we mean only that it is applicable to any one, without respect of individuals, either in predication or epithetic description.]

[Footnote 4: Strictly speaking, as I have tried to indicate all along, the words Connotation and Denotation, or Extension and Intension, apply only to general names. Outside general names, they have no significance. An adjective with its noun is a general name, of which the adjective gives part of the Connotation. If we apply the word connotation to signify merely the suggestion of an attribute in whatever grammatical connexion, then an abstract name is undoubtedly as much connotative as an adjective. The word _Sweetness_ has the same meaning as _Sweet_: it indicates or signifies, conveys to the mind of the reader the same attribute: the only difference is that it does not at the same time indicate a subject in which the attribute is found, as _sweet apple_. The meaning is not _con_noted.]

CHAPTER II.

THE SYLLOGISTIC ANALYSIS OF PROPOSITIONS INTO TERMS.

I.--THE BARE ANALYTIC FORMS.

The word "term" is loosely used as a mere synonym for a name: strictly speaking, a term ([Greek: horos], a boundary) is one of the parts of a proposition as analysed into Subject and Predicate. In Logic, a term is a technical word in an analysis made for a special purpose, that purpose being to test the mutual consistency of propositions.

For this purpose, the propositions of common speech may be viewed as consisting of two TERMS, a linkword called the copula (positive or negative) expressing a relation between them, and certain symbols of quantity used to express that relation more precisely.

Let us indicate the Subject term by S, and the Predicate term by P.

All propositions may be analysed into one or other of four forms:--

All S is P, No S is P, Some S is P, Some S is not P.

All S is P is called the UNIVERSAL AFFIRMATIVE, and is indicated by the symbol A (the first vowel of Affirmo).

No S is P is called the UNIVERSAL NEGATIVE, symbol E (the first vowel of Nego).

Some S is P is called the PARTICULAR AFFIRMATIVE, symbol I (the second vowel of _aff_Irmo).

Some S is not P is called the PARTICULAR NEGATIVE, symbol O (the second vowel of _neg_O).

The distinction between Universal and Particular is called a distinction in QUANTITY; between Affirmative and Negative, a distinction in QUALITY. A and E, I and O, are of the same quantity, but of different quality: A and I, E and O, same in quality, different in quantity.

In this symbolism, no provision is made for expressing degrees of particular quantity. _Some_ stands for any number short of all: it may be one, few, most, or all but one. The debates in which Aristotle's pupils were interested turned mainly on the proof or disproof of general propositions; if only a proposition could be shown to be not universal, it did not matter how far or how little short it came. In the Logic of Probability, the degree becomes of importance.

Distinguish, in this Analysis, to avoid subsequent confusion, between the Subject and the Subject Term, the Predicate and the Predicate Term. The Subject is the Subject Term quantified: in A and E,[1] "All S"; in I and O, "Some S". The Predicate is the Predicate Term with the Copula, positive or negative: in A and I, "is P"; in E and O, "is not P".

It is important also, in the interest of exactness, to note that S and P, with one exception, represent general names. They are symbols for classes. P is so always: S also except when the Subject is an individual object. In the machinery of the Syllogism, predications about a Singular term are treated as Universal Affirmatives. "Socrates is a wise man" is of the form All S is P.

S and P being general names, the signification of the symbol "is" is not the same as the "is" of common speech, whether the substantive verb or the verb of incomplete predication. In the syllogistic form, "is" means _is contained in_, "is not," _is not contained in_.

The relations between the terms in the four forms are represented by simple diagrams known as Euler's circles.

[Illustration:

1 concentric circles of P and S - S in centre A 2 S and P in the same circle A 3 S and P each in a circle, overlapping circle. I & O 4 S in one circle and P in another circle. E 5 concentric circles of S and P - P in centre I?

Diagram 5 is a purely artificial form, having no representative in common speech. In the affirmations of common speech, P is always a term of greater extent than S.

No. 2 represents the special case where S and P are coextensive, as in All equiangular triangles are equilateral.

S and P being general names, they are said to be DISTRIBUTED when the proposition applies to them in their whole extent, that is, when the assertion covers every individual in the class.

In E, the Universal Negative, both terms are distributed: "No S is P"

wholly excludes the two classes one from the other, imports that not one individual of either is in the other.

In A, S is distributed, but not P. S is wholly in P, but nothing is said about the extent of P beyond S.

In O, S is undistributed, P is distributed. A part of S is declared to be wholly excluded from P.